Let f (x) be a polynomial of degree two which is positive for all `x in R.` If `g(x)=f(x)+f(x)+f prime prime(x)+xf prime prime prime(x)+x^2 f^(iv) (x)` then for any real x, prove that `g(x) > 0.`

Let f(x) be a polynomial of degree two which is positive for all x in R. If g(x)=f(x)+f(x)+f'(x)+xf''(x)+x^(2)f^(iv)(x) then for any real x,prove that g(x)>0

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

Suppose that f(x) is a quadratic expresson positive for all real x If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x (where f^(prime)(x) and f^(primeprime)(x) represent 1st and 2nd derivative, respectively). (a) g(x) 0 (c). g(x)=0 (d). g(x)geq0

Suppose that f(x) is a quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(primeprime)(x), then for any real x (where f^(prime)(x) and f^(primeprime)(x) represent 1st and 2nd derivative, respectively). (a) g(x) 0 (c). g(x)=0 (d). g(x)geq0

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(x), then for any real x(w h e r ef^(prime)(x)a n df^(x) represent 1st and 2nd derivative, respectively). g(x) 0 c. g(x)=0 d. g(x)geq0

If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f^(prime)(x)g^(prime)(x)h^(prime)(x)f^(x)g^(x)h^(x)|i sacon s t a n tpol y nom i a l